The incident reportedly took place in Parwan Province Friday with Hezb-e-Islami group loyal to warlord Gulbuddin Hekmatyar immediately claiming responsibility for the attack.
The militant group said several American troops were killed in the deadly assault on the heavily fortified air field near Kabul. However, the US-led military alliance has not confirmed any casualties as a result of the rocket attack.
Bagram is home to thousands of US military personnel and civilian contractors.
The airbase has come under numerous rocket attacks since it was set up by the US army after it occupied Afghanistan more than eleven years ago.
Violence in Afghanistan has been on the rise in recent months despite the presence of thousands of US-led foreign forces in the war-weary country.
There has been no letup in the Taliban attacks on US-led foreign troops across Afghanistan with US-led troops and Afghan forces falling prey to Taliban attacks on an almost daily basis.
At least 3,391 US-led troops in Afghanistan have lost their lives since the 2001 invasion -- which was launched with the official objective of curbing militancy and bringing peace and stability to the country.
The increasing number of military casualties in Afghanistan has caused widespread anger in the US and other NATO member states, undermining public support for the Afghan war.
The offensive removed the Taliban from power, but years into the invasion, insecurity continues to rise across the country.
SHI/SHI